In the city center it is nearly impossible to find free parking areas during Onion Market
During those three a central parking area is to be found at the Kaufland supermarket - Humboldtstraße
A Park+Ride-possibilty - is available every 20 minutes til late night.
The price for parking (6,00 €) also covers the bus ride to the city and back.
http://www.weimar.de/en/tourismus/culture-leisure/markets-festivals/onion-market/parking/20. June 2013